Leaf Cleanup

While solving problem C, you may have learned about the results of cleaning Evstigraf's yard. This problem focuses on the process instead of the result.

During the cleaning, one of the main challenges was gathering the leaves that had fallen on the ground into piles that would satisfy Evstigraf. In total, $n$ piles were collected, and the $i$-th pile contains exactly $a_i$ leaves. The piles were then shown to Evstigraf.

Evstigraf does not want to spend time checking every pile, so he evaluates the work with this rule:

1. First, he asks you to name a contiguous range of exactly $k$ integers, that is, some $[l, r]$ with $r - l + 1 = k$.
2. Then he computes the sum of the sizes of the piles that fall into this range: $S = \sum_{l \leqslant a_i \leqslant r} a_i$.

The lower the value of $S$, the better the cleaning. Help the cleaners choose $l$ and $r$ so that $S$ is as small as possible. $l$ and $r$ cannot be negative or too large: $1 \leqslant l \leqslant r \leqslant c$ must hold for the given $c$.

The first line contains three integers $n$, $c$, and $k$ separated by spaces: the number of piles, the upper bound on the chosen range, and the length of the range ($1 \leqslant n \leqslant 10^5$; $1 \leqslant k \leqslant c \leqslant 10^9$).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$, the sizes of the piles ($1 \leqslant a_i \leqslant 10^9$).

Print one number: the minimum possible value of the sum described above.